Many devices, including a semiconductor exposure apparatus, are known as a device arranged to position an object on a stage, by which the stage moves on a surface plate. To increase the throughput using these devices, it is necessary to move an object on the stage as fast as possible. However, when the object on the stage is driven at high speed, mechanical resonance of the stage is excited, thereby deteriorating the alignment precision. This deterioration in alignment precision poses a serious problem, especially in a device which demands a high alignment precision in stage movement, such as a scanning exposure apparatus, numerically controlled processing equipment, and the like. For this reason, it is required to meet, in a balanced manner, demands for high-speed stage movement and demands for a high alignment precision.
Mechanical resonance which may occur in stage driving can be suppressed using, e.g., a notch filter. For example, in Japanese Patent Laid-Open No. 5-19858, a frequency-swept AC signal is superposed on a speed command value with respect to the speed control system of a servo actuator, and a frequency at which the amplitude of a torque command value decreases is used as the cutoff frequency of the notch filter. In Japanese Patent Laid-Open No. 5-159492, a notch filter is selected such that the peak of the amplitude of a response signal becomes small when a sine wave is input.
Japanese Patent Laid-Open No. 5-114141 describes a method of calculating the coefficients of a digital notch filter from the characteristic data of a predetermined optical pickup with respect to the tracking servo control system of an optical disk device. Additionally, in Japanese Patent Laid-Open No. 5-35335, a plurality of resonance elimination filters with slightly different cutoff frequencies and cutoff peak values are prepared for a stage control apparatus, and a filter with a cutoff frequency near the resonance frequency is selected when resonance occurs.
However, if a conventional notch filter is employed, a vibration signal needs to be externally superposed on a control system. Hence, a vibration device must separately be provided, and measurement of the resonance frequency and setting of the notch filter must be switched. Also, the mechanical resonance frequency of the stage varies depending on the stage, and thus the cutoff frequency of the notch filter must be adjusted for each stage. If a plurality of resonance elimination filters are used, the coefficients of the plurality of filters must be held as a table. Additionally, if the mechanical resonance frequency has a plurality of peak values, the coefficients of the notch filter must be adjusted for the respective peak values.